Match each whole number with a rational exponential expression. HELPP ME PLEEASE FASTTT
Answers
3rdrt[(343(343)]
49
2. [2,197^(1/3)]^2
[3rdrt(2,197)]^2
169
3. 729^(2/3)
3rdrt[729(729)]
81
4. (1,000^2)^(1/3)
3rdrt(1,000^2)
100
5. [3rdrt(9261)]^2
441
6. [3rdrt(216^2)]
36
Hope this helps!
Answer:
1. 49
2. 169
3. 81
4. 100
5. 441
6. 36
Step-by-step explanation:
1. [tex](343)^{\frac{2}{3}}=\sqrt[3]{(343)^{2} }[/tex]
= [tex]\sqrt[3]{(343)(343)}=\sqrt[3]{(7^{3})(7)^{3}}[/tex]
= 7×7 = 49
2. [tex](2197^{\frac{1}{3}})^{2}=(\sqrt[3]{2197})^{2}[/tex]
= [tex](\sqrt[3]{13^{3}})^{2}=13^{2}[/tex]
= 169
3. [tex]729^{\frac{2}{3} }=(\sqrt[3]{729})^{2}[/tex]
= [tex](\sqrt[3]{9^{3}})^{2} = 9^{2}[/tex]
= 81
4. [tex](1000^{2})^{\frac{1}{3}}=(\sqrt[3]{1000})^{2}[/tex]
= 10²
= 100
5. [tex](\sqrt[3]{9261})^{2}=(\sqrt[3]{(21)^{3} })^{2}[/tex]
= 21²
= 441
6. [tex](\sqrt[3]{216})^{2}=(\sqrt[3]{6^{3} })^{2}[/tex]
= 6²
= 36
Related Questions
Find the value of the missing side of a triangle practice
Answers
Be sure to understand the differences between a right-angled triangle and an irregular-shaped triangle.
Right-angled triangle
Two sides must be known.
[tex] {a}^{2} = {b}^{2} + {c}^{2} [/tex]
where 'a' squared is the hypotenuse of the triangle.
To find the non-hypotenuse side, the formula can be rearranged to
[tex] {b}^{2} = {a}^{2} - {c}^{2} [/tex]
'b' can be any non-hypotenuse side.
Non-right angled triangle.
Cosine rule
Two sides and an angle must be know.
[tex]a = {b}^{2} + {c }^{2} - 2ab \cos(angle \: facing \: a) [/tex]
That is just a few of the formulas I have listed.
The perimeter of a rectangle is 42 inches. If the length of the rectangle is 14 inches, which equation could be used to find the width, x? A. 2(x + 14) = 42 B. x + 2(14) = 42 C. 14(x + 2) = 42 D. x + 14 = 42
Answers
(2x = 14
x = 7
2(7) + 2(14) = 14 + 28 = 42)
Answer:
Option A is correct
equation [tex]2(x+14)=42[/tex] could be used.
Step-by-step explanation:
Given: The length of a rectangle [tex](l)[/tex] is 14 inches and perimeter of rectangle is 42 inches.
Perimeter(P)of a rectangle in inches is given by:
[tex]P= (2l+w)[/tex] ; where [tex]l[/tex] is the length of the rectangle and w is the width of the rectangle.
Substitute the value of P=42 inches , w =x inches and [tex]l = 14[/tex] inches in the above formula we get;
[tex]42 = 2 \cdot (14+x)[/tex]
Divide by 2 on both sides we get;
[tex]21 = 14+x[/tex]
On simplify, we get;
x = 21-14 = 7 inches
therefore, the width of the rectangle is, x = 7 inches
Check :
Substitute the value of x =7 in option A.
[tex]2(x+14) =42[/tex]
[tex]2(7+14)=42[/tex]
[tex]2\cdot 21 =42[/tex]
42 = 42
Hence, the only equation that could be used to find the width, x is, [tex]2(x + 14) = 42[/tex]
what is the slope of the line through (2,-2) and (9,3)
Answers
Twenty-seven minus of a number (x) is not more than 36. What is the number? x > 42 x ≥ -6 x < 3 x ≤ -6
Answers
54 - 3x ≤ 72
-3x ≤ 72 - 54
-3x ≤ 18
x ≥ 18/(-3)
x ≥ -6
..........................................................
The profits of mr cash’s company is represented by the equation p(t)=-3t^2+18t-4, where p(t) is the amount of profit in hundreds of thousands of dollars and t is the number of years of operation. he realizes his company is on the down turn and wishes to sell before he ends up in debt. in what year of operation does mr cash’s business show the maximum profit?
Answers
Explanation:
Note that p(t) is a quadratic function and so its graph is a parabola. Since the coefficient of t² in p(t) is negative, the maximum point in p(t) exist at its vertex. Moreover, the maximum value of p(t) is the y-coordinate of its vertex.
Note that p(t) can be expressed as:
[tex]p(t) = a(t-h)^2 + k [/tex] (1)
Where (h, k) are the coordinates of the vertex of p(t).
To manipulate p(t) in the form expressed in equation (1), we factor out the coefficient of t² in p(t) so that
[tex]p(t) = -3t^2+18t-4 \\ \boxed{p(t) = -3 \left( t^2 - 6t + \frac{4}{3} \right)}[/tex]
Then, we let
[tex]q(t) = t^2 - 6t + \frac{4}{3}[/tex]
So that
[tex]p(t) = -3q(t)[/tex] (2)
We need q(t) to be expressed as the sum of a perfect square trinomial and a constant. To form the perfect square trinomial in q(t), we can find a constant k such that [tex]t^2 - 6t + k [/tex] is a perfect square.
To find the value of k, we divide the coefficient of t by 2 and get the square of the result. Since the coefficient of t in q(t) is -6,
[tex]k = \left( \frac{-6}{2} \right)^2 = 9[/tex]
To avoid changing the value of q(t), if we add the constant k = 9, we need to subtract it by the same number. Since k = 9,
[tex]q(t) = t^2 - 6t + \frac{4}{3} + k - k \\ = t^2 - 6t + \frac{4}{3} + 9 - 9 \\ = (t^2 - 6t + 9) + \frac{4}{3} - 9 \\ \boxed{q(t) = (t - 3)^2 - \frac{23}{3}} [/tex]
From equation (2),
[tex]p(t) = -3q(t) \\ p(t) = -3\left( (t - 3)^2 - \frac{23}{3} \right) \\ \boxed{p(t) = -3 (t - 3)^2 + 23}[/tex]
Hence the vertex of p(t) is (3, 23) and maximum value is attained at t = 3. Therefore, the Mr. Cash's business has maximum profit at the 3rd year of operation.
Could someone explain this to me?
Answers
[tex]5y^4\frac{dy}{dx}+6y^2x+6x^2y\frac{dy}{dx}+20x^3 = 0[/tex]
Simplify:
[tex] \frac{dy}{dx} (5y^4+6x^2y) + 6y^2x+20x^3 = 0[/tex]
Solve for dy/dx:
[tex] \frac{dy}{dx} = \frac{-6y^2x-20x^3}{5y^4+6x^2y} [/tex]
Now, plug in the given points:
[tex]\frac{dy}{dx} = \frac{-6(2)^2(-1)-20(-1)^3}{5(2)^4+6(-1)^2(2)} = \frac{24+20}{80+12}[/tex]
Further simplification gives:
[tex]\frac{dy}{dx}|_{(2,-1)} =\frac{44}{92} = \frac{11}{23} [/tex]
So, your answer is 11/23 or B.
The prime factorization of a number is 2^3*3^2*5. Which is a true statement about the factors of the number?
1. Fifteen is a factor of the number because both 3 and 5 are prime factors.
2. Fifteen is not a factor of the number because 15 is odd and the number is even.
3. Sixteen is a factor for the number because 2^3=8 and 16 is divisible by 8.
4. Sixteen is not a factor of the number because the exponent of 2 is not even.
Answers
3^2 = 9
8 * 9 * 5 = 360
15 is a factor of 360, so the answer would be 1. Fifteen is a factor of the number because both 3 and 5 are prime factors
Fifteen is a factor of the number because both 3 and 5 are prime factors and this can be determined by using the arithmetic operations.
Given :
Number -- [tex]2^3\times 3^2\times 5[/tex]
The following steps can be used in order to determine the correct statement:
Step 1 - Write the given number.
[tex]2^3\times 3^2\times 5[/tex]
Step 2 - Simplify the above expression.
[tex]= 8\times 9 \times 5[/tex]
Step 3 - Multiply 8 by 9 in the above expression.
[tex]= 72\times 5[/tex]
Step 4 - Multiply 72 by 5 in the above expression.
= 360
Step 5 - 15 is a factor of 360.
Therefore, the correct option is 1).
For more information, refer to the link given below:
https://brainly.com/question/10454590
An investment of $750 will be worth $1500 after 12 years of continuous compounding at a fixed interest rate. What percent is the interest rate?
Answers
Final answer:
The interest rate is 100%, or 1 as a decimal, for continuously compounded interest.
Explanation:
To find the interest rate, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the final amount ($1500)P is the principal amount ($750)r is the interest rate (unknown)n is the number of times interest is compounded per year (continuously compounded)t is the time in years (12)Using the given information, we can plug in the values and solve for r:
$1500 = $750(1 + r/1)^(1*12)$2 = 1 + rr = $2 - 1 = $1The interest rate is 100%, or 1 as a decimal, for continuously compounded interest.
The interest rate, for continuous compounding, is approximately 5.775%.
To find the interest rate for continuous compounding, we can use the formula for compound interest:
[tex]\[ A = P \times e^{rt} \][/tex]
Where:
- [tex]\( A \)[/tex] is the final amount of money,
- [tex]\( P \)[/tex] is the principal amount (initial investment),
- [tex]\( r \)[/tex] is the interest rate (annual rate in decimal),
- [tex]\( t \)[/tex] is the time the money is invested for (in years),
- [tex]\( e \)[/tex] is the base of the natural logarithm, approximately equal to 2.71828.
Given:
- [tex]\( P = $750 \)[/tex],
- [tex]\( A = $1500 \)[/tex],
- [tex]\( t = 12 \)[/tex] years.
We need to solve for [tex]\( r \)[/tex], the interest rate.
Step 1 :**Substitute the Given Values into the Formulaa :
[tex]\[ 1500 = 750 \times e^{12r} \][/tex]
Step 2 :**Divide Both Sides by 750**:
[tex]\[ \frac{1500}{750} = e^{12r} \][/tex]
[tex]\[ 2 = e^{12r} \][/tex]
Step 3 :**Take the Natural Logarithm of Both Sides**:
[tex]\[ \ln(2) = \ln(e^{12r}) \][/tex]
[tex]\[ \ln(2) = 12r \ln(e) \][/tex]
[tex]\[ \ln(2) = 12r \][/tex]
Step 4 :**Solve for [tex]\( r \)[/tex]**:
[tex]\[ r = \frac{\ln(2)}{12} \][/tex]
[tex]\[ r = \frac{0.693}{12} \][/tex]
[tex]\[ r = 0.05775 \][/tex]
Step 5 :**Convert the Interest Rate to a Percentage**:
[tex]\[ r_{\text{percentage}} = 0.05775 \times 100\% \][/tex]
[tex]\[ r_{\text{percentage}} = 5.775\% \][/tex]
So, the interest rate is approximately 5.775%.
helpppppppppppppppppppppppp
Answers
[tex] x^{2} -2x-3[/tex] to do this we'll need to find two number whose product is -3 and its sum is -2; those numbers are 1 and -3, so:
[tex] x^{2} -2x-3=(x+1)(x-3)[/tex]
Now we can rewrite our rational function as follows:
[tex]f(x)= \frac{x-3}{(x+1)(x-3)} [/tex]
Notice that we have a common factor (x-3) in both numerator and denominator; therefore we can cancel them:
[tex]f(x)= \frac{1}{x+1} [/tex]
Taking all the above into consideration we realize that x=3 is a removable discontinuity; the correct answer is the first one: there is a hole in x=3 and asymptote at x=-1.
What is the approximate area of the circle shown below 60cm
Answers
This is the answer your welcome
Answer:
[tex]\text{Hence, the approx. area of circle }2827 cm^2[/tex]
Step-by-step explanation:
Given the diameter of circle 60 cm
we have to find the area of circle
Diameter=60 cm
Radius=30 cm
[tex]\text{Area of circle=}\pi r^2[/tex]
[tex]=\frac{22}{7}\times (30)^2=2828.57143\sim 2827(approx)[/tex]
[tex]\text{Hence, the approx. area of circle }2827 cm^2[/tex]
Option A is correct
Ryanne is 14. her brother's age is three more than half her age. how old is her brother?
Answers
half her age : 14 ÷ 2 = 7
three more : 7 + 3 = 10
Her brother is 10 years old.
Answer:
10 years old
Step-by-step explanation:
I will use the letter r to denote Ryanne's age:
r = 14
And according to the problem, her brother's age is THREE MORE THAN HALF HER AGE
so, we start by finding how much is half of Ryanne's age:
r/2 = 14/2 = 7
and next, we find that three more than half her age is:
7 + 3 = 10
Her brother is 10 years old
Answers anybody???????
Answers
.. As = (1/2)*r^2*(5π/6)
The area of the white triangle in that sector is
.. At = (1/2)*r^2*sin(5π/6)
The orange shaded area is the difference between these.
.. A = As -At = (1/2)*r^2*(5π/6 -sin(5π/6))
.. = (1/2)*(27.8 in)^2*(5π/6 -1/2)
.. A ≈ 818.4 in^2
table Mary used Delicious (d) and Golden Delicious (g) apples to make homemade applesauce. Delicious apples are $0.75 each and Golden Delicious apples are $1.25 each. Mary spent $21.00 on 22 apples. How many Golden Delicious apples did Mary buy?
Answers
2. The equations are:
d+g=22 (i)
0.75d+1.25g=21 (ii)
3. If you clear "d" from the equation (i), you have:
d+g=22
d=22-g
4. Now, you must substitute d=22-g into the equation (ii):
0.75d+1.25g=21
0.75(22-g)+1.25g=21
5. When you clear "g", you obtain its value:
16.5-0.75+1.25g=21
16.5+0.5g=21
0.5g=21-16.5
g=4.5/0.5
g=9 Golden Delicious apples
6. If you also want to know the value of "d", you can substitute g=9 into the equation (i) and clear "d":
d+g=22
d+9=22
d=22-9
d=13 Delicious apples
How many Golden Delicious apples did Mary buy?
The answer is: Mary bought 9 Golden Delicious apples.
Tldr: The answer is 9
How many pieces of pie will you have if 4 banana caramel cream pies are sliced into 1 8 servings? A) 12 B) 18 C) 24 D) 32
Answers
When 4 banana caramel cream pies are sliced into 1/8 servings, the number of pieces of pie obtained is 32.
Explanation:To determine the number of pieces of pie obtained when 4 banana caramel cream pies are sliced into 1/8 servings, we need to find the total number of pie servings. Each pie is sliced into 1/8 servings, so if we have 4 pies, we can calculate the total number of servings by multiplying 4 by 1/8.
4 x 1/8 = 4/8 = 1/2Therefore, we will have 1/2 pie when 4 banana caramel cream pies are sliced into 1/8 servings. Since 1/2 pie is equivalent to 4/8 pie, the answer is D) 32 pieces.
Can someone help me please I would appreciate it.
I well mark brainliest if u explain
Please.
Answers
A metal Fabricating Company produces 150,000 souvenir tokens each year. In a random sample of 400 tokens, 3 have stamping errors. Predict the total number of coins that will have stamping errors in a year.
Answers
150000 divided by 400 equals 375, times 3 equals 1125.
30 POINTS + BRAINLIEST!
Answers
We have to find the value of 'x' in [tex] \sin (x+22)^{\circ}=\cos (2x-7)^{\circ} [/tex]
By using the complementary angle formula which states:
[tex] \cos (90-\Theta )=\sin \Theta [/tex]
Now,
[tex] \cos (90^{\circ}-(x+22)^{\circ})=\cos (2x-7)^{\circ} [/tex]
Therefore, we get
[tex] 90-(x+22)= (2x-7) [/tex]
[tex] 90-x-22= (2x-7) [/tex]
[tex] 68=3x -7 [/tex]
[tex] 75=3x [/tex]
[tex] x=25^{\circ} [/tex]
Answer:
Lets go by a step-by-step process.
Step-by-step explanation:
\cos (90-\Theta )=\sin \Theta
Now,
\cos (90^{\circ}-(x+22)^{\circ})=\cos (2x-7)^{\circ}
Now we have...
90-(x+22)= (2x-7)
90-x-22= (2x-7)
68=3x -7
75=3x
x=25^{\circ}
PLEASE HELP
7.03
1. Write the sum using summation notation, assuming the suggested pattern continues.
1 - 3 + 9 - 27 + ...
A) summation of one times three to the power of n from n equals zero to infinity
B) summation of one times three to the power of the quantity n plus one from n equals zero to infinity
C) summation of one times negative three to the power of n from n equals zero to infinity
D) summation of one times negative three to the power of the quantity n plus one from n equals zero to infinity
2. Write the sum using summation notation, assuming the suggested pattern continues.
-4 + 5 + 14 + 23 + ... + 131
A) summation of the quantity negative four plus nine n from n equals zero to fifteen
B) summation of negative thirty six times n from n equals zero to fifteen
C) summation of the quantity negative four plus nine n from n equals zero to infinity
D) summation of negative thirty six times n from n equals zero to infinity
3. Write the sum using summation notation, assuming the suggested pattern continues.
25 + 36 + 49 + 64 + ... + n2 + ...
A) summation of n squared from n equals five to infinity
B) summation of n minus one squared from n equals five to infinity
C) summation of n squared from n equals six to infinity
D) summation of n plus one squared from n equals five to infinity
4. Find the sum of the arithmetic sequence.
-1, 2, 5, 8, 11, 14, 17
A) 56
B) 63
C) -7
D) 20
5. Find the sum of the geometric sequence.
1, one divided by four, one divided by sixteen, one divided by sixty four, one divided by two hundred and fifty six
A) 341
B) one divided by one hundred and ninety two
C) one divided by seven hundred and sixty eight
D) three hundred and fourty one divided by two hundred and fifty six
6. Find the sum of the first 8 terms of the sequence. Show all work for full credit.
1, -3, -7, -11, ...
Answers
1, -3, -7, -11, -15, -19, -23, -27...
sum:
8/2 (1 + -27)
8/2 (-26)
-104
Problem 1. Write the sum using summation notation, assuming the suggested pattern continues.
1 - 3 + 9 - 27 + ...
Answer: option C) summation of one times negative three to the power of n from n equals zero to infinity
Explanation:
1) Sequence: 1 - 3 + 9 - 27: given
2) ratio of two consecutive terms:
- 3 / 1 = - 3
9 / (-3) = - 3
-27 / (9) = - 3
=> ratio = - 3 means that every term is the previous one multiplied by - 3
3) terms
First term: 1 * (-3)^0 = 1
Second term: 1* (-3)^1 = - 3
Third term: 1 * (-3)^2 = 9
Fourth term: 1 * (-3)^3 = - 27
So, the summation is:
∞
∑ 1 * (-3)^n ,
n=0
which is read summation of one times negative three to the power of n from n equals zero to infinity => option C.
Problem 2. Write the sum using summation notation, assuming the suggested pattern continues.
- 4 + 5 + 14 + 23 + ... + 131
Answer: option A) summation of the quantity negative four plus nine n from n equals zero to fifteen
Probe the statement A):
15
∑ (- 4 + 9n)
n=0
Now develop that summation: - 4 +9(0) - 4+ 9(1) - 4 + 9(2) - 4 + 9(3) +....+ - 4 + 9(15) = - 4 + 5 + 14 + 23 + 131
Which is the very same sequence given.Therefore, the first statement if right.
Problem 3. Write the sum using summation notation, assuming the suggested pattern continues.
25 + 36 + 49 + 64 + ... + n^2 + ...
Answer: option A) summation of n squared from n equals five to infinity
Explanation
First term: 25 = 5^2
Second term: 36 = 6^2
Third term: 49 = 7^2
Fourth term: 64 = 8^2
nth term n^2
last term: the sequence is infinite
So, you can see that the sequence is the sum of the square of the integers from n = 5 to infinity =
∞
∑ (n^2)
n = 5
which is what summation of n squared from n equals five to infinity means.
Problem 4. Find the sum of the arithmetic sequence.
-1, 2, 5, 8, 11, 14, 17
Answer: option A) 56
Explanation:
You just have to sum all the terms (since they are few numbers that is the best way): - 1 + 2 + 5 + 8 + 11 + 14 + 17 = 56
Answer: 56
Problem 5. Find the sum of the geometric sequence.
1, one divided by four, one divided by sixteen, one divided by sixty four, one divided by two hundred and fifty six
Answer: option D) 341 / 256
Explanation:
Write in form of fractions: 1 + 1/4 + 1/16 + 1/64 + 1/256
You'd better use the formula for the summation of a geometric sequence
k
∑ A * (r^n) = A * (1 - r^k) / (1 - r)
n=1
In this case: r = 1/4 (the ratio)
k = 5 (the number of terms)
A = 1 (the first term)
=> The sum = 1 * [1 - (1/4)^5 ] / [ 1 - 1/4], which when you simplify turns into 341 / 256 which is the option D.
Problem 6. Find the sum of the first 8 terms of the sequence. Show all work for full credit.
1, -3, -7, -11, ...
Answer: - 104
Explanation:
You can either sum the 8 terms or use the formula for the sum of an aritmetic sequence.
I will sum the 8 terms.
Note the the constant distance to sum is - 4, so the sum of the first eight terms is:
1 - 3 - 7 - 11 - 15 - 19 - 23 - 27 = - 104
Which graph represents y – 1 = 2(x – 2)?
Answers
Answer:
The graph is attached below
Step-by-step explanation:
y – 1 = 2(x – 2)
y-1 = 2x - 4
add 1 on both sides
y = 2x - 3
To graph the given equation we make a table
Plug in some number for x and find out the value of y
x y = 2x-3
-1 2(-1)-3= -5
0 2(0) -3= -3
1 2(1) -2= -1
The point to get the graph of the given equation is
(-1,-5) (0,-3) (1,-1)
The graph is attached below
Answer:
The answer is the first graph or graph A.
BTW this is just the short answer...
Its quicker. :-)
the width of an architects desk is represented by four times x squared and the length is represented by the expression 2x cubed. what represents the area of the tabletop
Answers
Does the equation x2 - 4x + y2 = -3 intersect the x-axis?
Answers
x^2 - 4x + 0 = -3
We then want to solve for x. We can do this by factoring.
x^2 - 4x + 3 = 0
By factoring...
(x - 3)(x - 1)
We can set each of these equations = 0 to solve where the function crosses the x-axis.
x - 3 = 0
x = 3
x - 1 = 0
x = 1
So we know at x = 1 and x = 3, the function x^2 - 4x + y^2 = -3 intersects the x-axis.
Answer:
Yes, because the center is on the x-axis.
Step-by-step explanation:
First, write the equation in standard form by completing the square.
x2 - 4x + y2 = -3
x2 - 4x + 4 + y2 = -3 + 4
(x - 2)2 + y2 = 1
The circle is centered at (2, 0) with a radius of 1. Since the circle is centered on the x-axis, it intersects the x-axis two times, at (3, 0) and (1, 0).
Which polynomial is a quintic trinomial?
x³ + 2x² -8x + 16
x² + 4
3x⁵ + 7x² -9x⁴
-x⁴ -5x² +1
Answers
Answer:
3x⁵ + 7x² -9x⁴
Step-by-step explanation:
In the order given, the polynomials have degrees 3, 2, 5, 4. The one of degree 5 is "quintic." That one also happens to be a trinomial. It is ...
3x⁵ + 7x² -9x⁴
What is the sum of the “outer” and “inner” products as described in the FOIL method when multiplying (x + 5)(x - 6)?
A. -6x
B. -x
C. x
D. 5x
Answers
The "inner" terms are +5 and x, so their product is 5x.
The sum of "outer" and "inner" terms is -6x +5x = -x. (selection B)
WILL GIVE A BRAINLEST!!!!!!
Solve and check : c-4/c-2=c-2/c+2 - 1/2-c
The solution is c =
How many extraneous solutions are there?
Answers
(c-4)/(c-2)=(c-2)/(c+2) - 1/(2-c)
- 1/(2-c)=-1/-(c-2)=1/(c-2)
(c-4)/(c-2)=(c-2)/(c+2)+ 1/(c-2)------- > (c-4)/(c-2)-1/(c-2)=(c-2)/(c+2)
(c-4-1)/(c-2)=(c-2)/(c+2)---------------- > (c-5)/(c-2)=(c-2)/(c+2)
(c-5)/(c-2)=(c-2)/(c+2)------------- > remember (before simplifying) for the solution that c can not be 2 or -2
(c-5)*(c+2)=(c-2)*(c-2)------------------ > c²+2c-5c-10=c²-4c+4
-3c-10=-4c+4----------------------------- > -3c+4c=4+10----------- > c=14
the solution is c=14
the domain of the function is (-∞,-2) U (-2,2) U (2,∞) or
all real numbers except c=-2 and c=2
The solution is c = 14
How many extraneous solutions are there? zero
What is the area of a sector with a central angle of π3 radians and a radius of 12.4 m? Use 3.14 for π and round your final answer to the nearest hundredth. Enter your answer as a decimal in the box.
Answers
Answer: [tex]80.47\ m^2 [/tex]
Step-by-step explanation:
The area of a sector is given by :-
[tex]\text{Area of sector}=\frac{\theta}{2}\times( r^2), \text{where }\theta\text{ is measure of central angle in radians.}[/tex]
Given :Central angle = [tex]\theta=\frac{\pi}{3}[/tex]
radius = 12.4 m
Then,
[tex]\text{Area of sector}=\frac{\frac{\pi}{3}}{2}\times( (12.4)^2)\\\\\Rightarrow\ \text{Area of sector}=\frac{\pi}{6}\times153.76\\\\\Rightarrow\ \text{Area of sector}=\frac{3.14}{6}\times153.76\\\\\Rightarrow\ \text{Area of sector}=80.4677333333\approx80.47\ m^2 [/tex]
Write an equation of the line pictured in the graph.
Answers
what is a possible value for the missing term of the geometric sequence ?
50, blank, 450, ..
a. 1,350
b. 150
c. 3
d. 53
Answers
So the answer is b 150
A FIELD HOCKEY TEAM IS A RECTANGLE 60YARDS BY 100YARDS .WHAT IS THE LENGTH OF THE DIAGONAL FROM ONE CORNER TO THE FIELD TO THE OPPOSITE CORNER ROUND YOUR ANSWER TO THE NEAREST HUNDRETH
Answers
3600 + 10000 = X^2
13600 = x^2
X = Sqrt(13600)
X = 116.619
Diagonal = 116.62 yards
3600 + 10000 = c^2
13600 = c^2
c = 116.62 yd
If c is a constant such that 9x^2+10x+c is equal to the square of a binomial, then what is c?
I NEED HELP SO BAD PLEASE PLEASE PLEASE
Answers
= 9x^2 + 6b x+ b^2
1) 6b= 10
b+ 5/3
2) c=b^2
c= (5/3) ^2
c= 25/9
(9x^2+10x+25/9)=(3x+5/3)^2
I hope this helps:)
A field project superintendent earns an annual salary of $72,800, and she contributes $7900 per year to her 401(k) plan. If she has a required deduction for income taxes (federal, state, and local combined) of 28% of pretax income, how much does she have withheld in income taxes per year?
Answers
What this means in terms of the question is that we should deduct the $7,900 first and then take 28% of what is left for taxes.
This person's salary is $72,800 a year and they set aside $7,900 for their retirement account (401K) so that leaves $72800-$7900 = $64,900
She now pays taxes of 28% on this amount ($64,900). Percent means "out of 100" so 28% means [tex] \frac{28}{100}=.28 [/tex] and to find 28% of 64900 we multiply (64900)(.28) = $18172.
That is she has $18,172 withheld in taxes each year.